Manuscript X-B-ST@1 · X-B-ST.tex · section · d03c150c

Action on the first dressing

The mixed term, second-order boundary, and diagnostics › Action on the first dressing · lines 1382–1405

X-B-ST@1#eq:c2change

For comparison, the supplied coordinate laws imply the bare-test identities

c_{1} [h^{'}] - c_{1} [h] c_{2} [h^{'}, k^{'}] - c_{2} [h, k] = D_{ξ} f, = D_{ξ} c_{1} [h] + \frac{1}{2} D_{ξ}^{2} f + D_{ζ} f .

To verify the second line algebraically, substitute (eq:coordinatelaw) into $B = w \cdot \partial w - v$ . It gives

B^{'} = B + w \cdot \partial ξ + \frac{1}{2} ξ \cdot \partial ξ - ζ .

The change of (eq:barecoeff) is then

\int f (X_{w} X_{ξ} ψ + \frac{1}{2} X_{ξ}^{2} ψ - X_{ζ} ψ) d^{4} x .

Transposition yields (eq:c2change).

Displayed formulas in this passage

X-B-ST@1#eq:c2change · line 1386
$c_{1} [h^{'}] - c_{1} [h] c_{2} [h^{'}, k^{'}] - c_{2} [h, k] = D_{ξ} f, = D_{ξ} c_{1} [h] + \frac{1}{2} D_{ξ}^{2} f + D_{ζ} f .$
unlabeled · line 1395
$B^{'} = B + w \cdot \partial ξ + \frac{1}{2} ξ \cdot \partial ξ - ζ .$
unlabeled · line 1400
$\int f (X_{w} X_{ξ} ψ + \frac{1}{2} X_{ξ}^{2} ψ - X_{ζ} ψ) d^{4} x .$